A Quantitative Examination of Trade andCarbon Taxes∗

Joshua Elliott† Ian Foster‡ Sam Kortum§

Todd Munson¶ Fernando Pérez Cervantes‖ David Weisbach∗∗

Preliminary. Subject to Revision.

June 14, 2010

Abstract

We examine the impact of carbon leakage on a regional carbon taxusing a newly developed, open-source computable general equilibriummodel, CIM-EARTH. We consider a business as usual scenario withhigh emissions because of rapid economic growth and slow adoptionof clean energy. Relative to our baseline scenario, a production taxin Annex B countries reduces emissions only by 1/3 of the emissionsreductions that would be achieved under a global carbon tax. This dueto the importance of emissions in developing countries in the futurerather than carbon leakage. Carbon leakage —the increase in emissionsin non-taxing regions relative to emissions reductions in taxing regions

∗This work was supported by grants from the MacArthur Foundation and the Universityof Chicago Energy Initiative and by the Offi ce of Advanced Scientific Computing Research,Offi ce of Science, U.S. Department of Energy, under Contract DE-AC02-06CH11357.†U. Chicago Computation Institute and Argonne National Laboratory, email:

jelliott@ci.uchicago.edu‡U. Chicago Computation Institute and Argonne National Laboratory, email:

foster@mcs.anl.gov§U. Chicago Economics, email: kortum@uchicago.edu¶U. Chicago Computation Institute and Argonne National Laboratory, email:

tmunson@mcs.anl.gov‖U. Chicago Economics, email: fernandoperez@uchicago.edu∗∗U. Chicago Law School, email: d-weisbach@uchicago.edu

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—ranges from 15% to 25%, depending on the tax rate. Border taxadjustments eliminate about half of the leakage.

1 Introduction

We examine the impact of carbon leakage on a regional carbon tax or equiva-lent carbon price. Carbon leakage results from an increase in emissions (overbusiness as usual emissions) in regions that do not have a carbon tax, forexample, because production shifts to those regions. Carbon leakage is cen-tral to understanding the economic effects of regional carbon tax because itcan result in ineffi cient location of production and can make regional carbontaxes futile. For similar reasons, carbon leakage will be central to the polit-ical negotiations over carbon controls, as politicians worry about job losses.The EU, for example, has announced that is will consider modifications to itscarbon trading system to limit leakage. Proposed cap and trade legislationin the United States often includes such measures and concerns about carbonleakage are often cited as reasons to oppose unilateral measures.The central policy response to carbon leakage is to impose border tax

adjustments, which are taxes on the import of carbon-intensive goods andrebates of taxes on export. If a nation imposes border tax adjustments,domestic producers will not be at a disadvantage relative to producers incountries without a carbon price. Border tax adjustments, however, will becomplex to administer because of the need to determine the embedded car-bon in traded goods. Moreover, they will be controversial because they looklike trade barriers, and because they may potentially be illegal under inter-national trade law. Imposing border tax adjustments risks retaliation fromcarbon-exporting countries. Therefore, unless carbon leakage is significantand border taxes are highly effective in reducing leakage, they are unlikelyto be desirable.Because of its importance there is a substantial literature on carbon leak-

age. Estimates vary widely, with the majority of estimates showing modesteffects, but some showing leakage in excess of 100%. For example, Mandersand Veendendaal (2008) use a CGE model similar to that used here and findmodest carbon leakage of about 3 percent from a policy to reduce emissionsin the EU in 2020 to 20 percent below 1990 levels. Applying full border taxadjustments within their model virtually eliminates carbon leakage. Aldy

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and Pizer (2008) use relative changes in fuel prices in a regression analy-sis to estimate the extent of carbon leakage and find rates consistent withManders and Veendendaal. In contrast, several studies using MIT’s EPPAmodel, which is also a CGE model similar to the model used here, find higherleakage rates. Babiker and Rutherford (2005) model the Kyoto Protocol inthe EPPA model and find substantial leakage and small effects from bordertaxes. Babiker (2005), uses EPPA to predict leakage in excess of 100 per-cent in one scenario, driven by an assumption of increasing returns to scale.Recent work by Mattoo et al. (2009) highlights how border tax adjustmentscould harm developing economies.There is also a substantial literature on the legality of border taxes ad-

justments in a carbon tax. The WTO and the United Nations EnvironmentProgramme recently released an analysis of the legality of border taxes, butafter extensive analysis of the relevant laws, does not draw any conclusions.WTO and UNEP (2009). Scholarly work on the issue is similarly ambigu-ous. Demaret and Stewardson (1994), Goh (2004), Ismer and Neuhoff(2007),Pauwelyn (2007), and Sindico (2008). Depending on which provisions of theGATT and WTO rules apply, border taxes may be limited to particularforms. The legal rules may allow full border taxes (tax on import, rebate onexport) but require them to be based on actual emissions during productionof traded goods. Alternatively, the legal rules may allow full border taxes butrequire them to be based on domestic emissions when producing like goodsor to be based on emissions when using the best available technology. Onsome readings of the relevant law, trade rules may allow only partial bordertaxes, such as a tax on imports but no rebate on exports. Because of thelegal uncertainty, any border tax regime will be controversial and will likelyto lead to high profile litigation.We address the problem using CIM-EARTH, a new, open-source, com-

putable general equilibrium model of the world economy. To develop basicintuitions, we first present a simple two-country, two-good model that wesolve analytically. This model reproduces well-known results from the taxliterature. For example, world-wide production and consumption taxes areequivalent in terms of their effects on the taxed activity; the location of taxcollection, upstream when fossil fuels are extracted or refined or when goodsare produced, or downstream on consumers, does not matter. Productionand consumption taxes, however, have distributional differences: countrieswell-endowed with energy prefer upstream (production) taxes. Moreover, aregional production tax on carbon combined with border tax adjustments is

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equivalent to a consumption tax.The literature on carbon leakage often refers to two distinct types of leak-

age: (i) leakage resulting from a shift in the location of production, and (ii)leakage resulting from an increase in consumption in non-taxing regions dueto the increased availability of fossil fuels. Both types of leakage are presentin our simple model, but they cannot both occur at the same time. In a con-sumption tax, the world price of energy and energy-related goods is drivendown because of a reduction in consumption in the taxing regions, resultingin an increase in consumption abroad. In a production tax, world energyprices are driven up resulting in an increase in production in non-taxing re-gions. Adding border taxes to a production tax, which in effect switches theproduction tax to a consumption tax, switches the type of leakage but cannoteliminate it.Within CIM-EARTH we consider four scenarios over a range of tax rates:

(i) a global carbon tax; (ii) a carbon tax on production in Annex B coun-tries only; (iii) a carbon tax in Annex B countries with complete border taxadjustments; and (iv) a partial border tax in which there is a tax on im-ports but not rebate on exports. In our simulations, a carbon tax only inAnnex B countries produces only about 1/3 of the reductions of the globalcarbon tax. This is, however, not primarily due to leakage; instead it reflectsthe importance of emissions from non-Annex B countries in 2020. Leakage,which we define as the increase in emissions in non-taxing regions relative tothe emissions reductions in taxing regions, is 15 to 25 percent, depending onthe tax rate. A border tax eliminates about half of this leakage, and shiftsthe source of the leakage from production decisions to changes in consump-tion patterns. These results are consistent with the predictions of the simplemodel; in particular, the type of leakage in CIM-EARTH depends on whetherthe tax is a consumption tax or a production tax and we do not, in mostcases, see both types of leakage occurring simultaneously.The simulations presented here are preliminary. In the final section of

the paper, we present our agenda for improvements to the model, focusingon improvements in the representation of trade and transport, carbon policymechanisms, model-agent expectations and foresight, and uncertainty. Wepresent here only point estimates and expect in the immediate future to con-sider uncertainty over the central parameters in the model affect our results;we emphasize that our point estimates should be taken only as suggestive.Section 2 of the paper presents the simple model and the derives the re-

sults we expect to see in CIM-EARTH based on intuitions from the simple

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model. Section 3 provides a system of carbon accounting, which we use toillustrate the trade in carbon dioxide and to calculate border taxes. Section4 give background on CIM-EARTH and presents our business as usual esti-mates. Section 5 turns to our simulations. Section 6 concludes and sets forthour research agenda for improving the modeling of this issue.

2 Basic Analytics

To motivate the problem and develop intuitions, we use a simple, two-countryillustration that is a special case of the standard 2x2x2 Heckscher Ohlin model(see, for example, Feenstra (2004)). We want to consider whether and howdifferent types of carbon taxes differ when imposed globally or locally.The countries are home and foreign, the factors are labor L and an energy

resource E, and the goods (sectors) are labor intensive Ql and energy inten-siveQe. As in the HOmodel, factors of production are perfectly mobile acrosssectors and immobile across countries. Markets are perfectly competitive.We make all the standard auxiliary assumptions: (i) common hometheticpreferences over the two goods in the two countries, (ii) common productiontechnology across countries, (iii) costless international trade, and (iv) no fac-tor intensity reversals so that at any factor prices production of the energyintensive good (true to its name) uses a higher ratio of E to L. Furthermore,we assume that relative endowments are similar enough so that both coun-tries produce both goods (the endowments are in the cone of diversification).We take emissions to be proportional to production of the energy-intensive

good. It might seem more natural to take emissions to be proportional to E,but in that case, emissions would be fixed based on the world endowment ofE, and could not be affected by a tax. It makes sense to think of emissionsas related to Qe if extraction of E takes effort.To keep the structure as simple as possible, we assume Cobb-Douglas

production functions where the energy-intensive good is produced using bothlabor and energy and the labor intensive good is produced using only labor:

Qe = (Le/β)β E1−β (1)

Ql = Ll. (2)

Preferences are identical in the two countries and Cobb-Douglas with shareα on the energy-intensive good:

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U = (Ce/α)α (Cl/(1− α))1−α . (3)

We take the labor-intensive good to be the numeraire, set its price to 1, andchoose units so that the wage in home and foreign is also 1. Let the price ofthe energy intensive good on the world market be p.In this setting, with no distortions, we get factor price equalization, i.e.

the wage for labor w and the rental price of the energy resource r are commonacross countries. With factor price equalization, the world economy behavesas if it were one integrated economy with factor endowments LW = LH +LF

and EW = EH + EF .We want to derive the price, quantity, and net exports of the energy-

intensive good. The following results hold for either country so we drop thesuperscript. Cobb-Douglas preferences imply constant expenditure shares sothat at price p, the marginal rate of substitution is:

ClCe

=1− αα

p. (4)

Equating the value of the marginal product of labor in the energy-intensivesector to the wage of one yields

LeE

= βp1/(1−β) (5)

Substituting (5) into the production functions:

Qe = pβ/(1−β)E (6)

which gives us the marginal rate of transformation:

Ql

Qe

=L− βp1/(1−β)E

pβ/(1−β)E. (7)

Since these expressions hold in either country, they also hold for theintegrated world economy. We can therefore evaluate (4) and (7) at worldendowments, solving for the equilibrium price p that equates CW

l /CWe and

QWl /Q

We :

p =

(αLW

[(1− α) + αβ]EW

)1−β

. (8)

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Substituting (8) into (6) gives us the global quantity of the energy-intensivegood without taxes:

QWe (0) =

(α

(1− α) + αβ

)β(LW )β(EW )(1−β),

The home country’s net exports of the energy-intensive good are:1

Ne = αLH(EH/LH

EW/LW− 1

). (9)

Thus, as implied by the famous Heckscher-Ohlin theorem, the home countryis a net exporter of the energy-intensive good exactly when it is relativelywell endowed with the energy resource.

2.1 Worldwide taxes

The goal is to reduce world carbon emissions through either a production taxor a consumption tax.2 A production tax, τ , is an ad valorem tax imposedupstream on production of the energy intensive good. A consumption tax,t, is imposed downstream on its consumption. The after-tax price paid byconsumers is pc = p(1 + t) and the price received by producers is pp =p/(1 + τ). Tax revenue is rebated in a lump sum to consumersWith worldwide taxes, the world economy continues to behave as if it

were one integrated economy. Because the world economy acts like a single,integrated economy, a consumption tax is equal to a production tax in terms

1The value of home’s net exports of the energy intensive good are

pQHe − pCHe = p1/(1−β)EH − αY H

= p1/(1−β)EH − α(LH + rEH)= p1/(1−β)EH − αLH − α(1− β)p1/(1−β)EH

= (1− α+ αβ)p1/(1−β)EH − αLH .

Substituting in (8) yields the result.2For taxes to have any effect on world production of the energy—intensive good, β must

be greater than zero. If β = 0 then a tax simply lowers the rents to owners of E as wouldbe the case if E were petroleum reserves that could be tapped at zero marginal cost. Inwhat follows, assume that β > 0 so that shifting labor out of the energy intensive sectorlowers emissions. Similarly, if α = 1, a tax simply raises the price of the energy intensivegood to consumers without reducing demand, so we assume α < 1.

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of the allocation of production; the only difference is how tax revenue isdistributed across countries. The country that is a net exporter of the energy-intensive good will prefer a production tax since it will then retain more taxrevenue.To see this result, consider a uniform production tax τ (with no con-

sumption tax). The consumption tradeoff (4) is unchanged while pp replacesp in the production equations (5), (6), and (7). The resulting equilibriumproducer price is

pp(τ) =

(αLW

[(1− α)(1 + τ) + αβ]EW

)1−β

, (10)

so that p(0)/(1 + τ) < pp(τ) < p(0). Adjusting (6) for taxes, we get worldproduction of the energy-intensive good:

QWe (τ) = pp(τ)β/(1−β)EW (11)

=

(α

(1− α)(1 + τ) + αβ

)β(LW )β(EW )(1−β), (12)

which is decreasing in the tax rate.With a consumption tax the production tradeoff (7) is unchanged while

pc replaces p in (4). The resulting equilibrium price is the same as pp(t).Hence a consumption tax of t leads to the same equilibrium world outputas a production tax at a rate of τ = t. Imposition of the tax upstream onproduction or downstream on production does not matter for the effect of thetax on output. Different countries, however, will receive the revenue from thetwo taxes, creating distributional differences. A production tax is beneficialto the country relatively well-endowed with E. Conversely, relative to aproduction tax, a consumption tax shifts the distribution of world incometoward the country relatively poorly endowed with E.We can use (12) to solve for the uniform tax rate required to lower global

emissions by a given factor λ = QWe (τ)/QW

e (0) < 1. Dividing QWe (τ) by

QWe (0), we get:

τ(λ) =

(1 +

αβ

1− α

)(λ−1/β − 1

). (13)

A higher tax rate is required when the energy-intensive good has a largershare in preferences (α is large). If labor has a small share in production of

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the energy-intensive good (β is small), then the tax rate is more sensitive tothe emissions reductions goal.We want to compare the results in this simple model with the results of

CIM-EARTH. To do this, we need to convert the ad valorem tax into anexcise tax rate e = pp(τ)τ/c where c is the carbon content of the energy—intensive good. We get:

e(λ) = γ

(1 +

αβ

1− α

)(1− λ1/β

λ

), (14)

where γ = p(0)/c, is the value of the energy-intensive good (at a zero carbontax) per unit of carbon.

2.2 Regional taxes

If a tax is imposed only in the home country, then the distinction betweena production tax and a consumption tax is crucial. A consumption tax timposed only in the home-country leaves pp = p in both countries so thereis no distortion of production decisions: Qe = pβ/(1−β)E. To equate worldsupply and demand, the tax drives down the equilibrium world price p, hencereducing production at home and abroad. The price faced by home consumerspc = (1 + t)p rises, reducing consumption in the home country which ispartially offset by an increase in consumption abroad.A home-country production tax τ , by contrast, leaves pc = p in both

countries so that there is no distortion of consumption. A production tax,however, drives up the equilibrium world price p. Consumers everywhere andforeign producers face a higher price than without a tax, so consumption inboth countries declines, but foreign production increases. The price faced byhome producers, pp = p/(1 + τ), declines by enough to outweigh an increasein production abroad.Production and consumption taxes both experience a form of carbon leak-

age. In a consumption tax, the world price is driven down because of thelower home-country consumption of the energy-intensive good and, corre-spondingly, foreign consumption increases. In a production tax, foreign pro-duction increases in response to the increase in the world tax. These twotypes of leakage correspond to the two types of leakage identified in the lit-erature: shifts in production location and increased consumption abroad. In

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our simple model, however, they do not both occur at the same time. In par-ticular, much of the literature associates a production tax with both typesof leakage, and this does not occur in the present setting.Home consumption is not necessarily higher under a nonglobal consump-

tion tax than under a nonglobal production tax that produces the sameemissions reductions. In fact, if the home country is well enough endowedwith E, its welfare is higher with the production tax. Nonetheless, if we takethe home country to be a net importer of the carbon-intensive good (thehome country, for example, might be the Annex B Kyoto region), then itwill prefer the consumption tax. A production tax, however, is vastly sim-pler to administer because of the relatively few sources of carbon emissionsthat would need to be taxed. Metcalf and Weisbach (2009)Because of the likely advantages of the consumption tax (if a global tax

is not adopted) and the practical advantage of production tax, some havetalked of a production tax with a border-tax adjustment (BTA). Consider aproduction tax at rate τ implemented only in the home country. A full BTAinvolves an export tax rebate for home’s producers and a tax τ on importsof the energy-intensive good. Such a BTA turns the production tax into aconsumption tax at rate τ . In equilibrium, pp = p, and pc = (1 + τ) p. Ifeither home or foreign producers supply consumers in the foreign country,the consumers will not face a tax, so pp = p. If either home country orforeign producers supply home consumers, there will be a wedge of τ , whichpc = (1 + τ) p satisfies.A full BTA brings implementation and possibly legal diffi culties, leading

some to advocate a production tax with a partial BTA involving either a taxon imports or a rebate for exports, but not both. Consider first a tax onimports of the energy-intensive good without the rebate on exports. If thehome country is relatively well endowed with E, then the tax on importsis irrelevant, and we are back to a simple production tax with pp = p/(1 +τ) and pc = p (and foreign producers of the energy-intensive good neversupplying home consumers). If the home country has little E, then the lackof a rebate on exports is irrelevant, and we are back to a simple consumptiontax with pp = p and pc = (1 + τ)p (and home producers of the energy-intensive good never supplying foreign consumers). If the home country hasa relatively moderate endowment of E, then the equilibrium will involve alltrade shutting down. In this case the equilibrium involves p/(1 + τ) < pp <p. Put differently, foreign energy-intensive good producers cannot sell tohome consumers since p(1 + τ) > pp(1 + τ), and home energy-intensive good

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producers cannot sell to foreign consumers since pp(1 + τ) > p. In this casethe partial border tax acts as a trade friction.A partial BTA with a rebate on exports but no tax on imports leads to

the possibility of an even more perverse outcome. In the middle range it caninduce cross hauling, with foreign energy-intensive good producers selling alltheir output to home producers and home energy-intensive good producersexporting all their output. This reduces the degree of carbon leakage thatwould occur from a simple production tax. Note that to have any effect, sucha tax must include a restriction on reimports. Otherwise home producerscould supply home consumers by shipping through the foreign country andback again. If this behavior is allowed, we return to a world of no taxes.

3 Estimating Trade in Carbon

Before turning to CIM-EARTH, we present calculations of the extent of tradein embedded carbon, which is the emissions from the production of a good.For example, suppose that CO2 is emitted during the production of a goodand the good is exported. The CO2 emitted during the production is embed-ded carbon and we treat it as traded when the good is traded, even thoughonly the good and not the CO2 is actually traded.To impose either a tax on consumption or a border tax, the tax authorities

must be able to determine embedded carbon. In the case of a consumptiontax, the embedded carbon is needed to impose the tax on the consumer onthe purchase. For example, to impose a carbon tax on the purchase of anautomobile, the tax authority must determine the emissions created duringthe production of the vehicle. Components of the vehicle may be producedin various places, assembled elsewhere, and the vehicle sold in yet a differentlocation. To determine the appropriate tax, we have to be able to trace thecarbon emitted during this production process. Similarly, if there are bordertax adjustments (with a production tax), the tax authority must know theembedded carbon of goods at the border to impose the border tax or rebate.Determining embedded carbon is also of stand-alone interest for those whobelieve that responsibility for emissions should be based on a consumptionmeasure rather than the traditional production measure used, for example,in the IPCC emissions inventory system. If we know embedded carbon andtrade flows, we can calculate emissions on a consumption basis.We provide details of this calculation in Appendix A and give only the

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intuitions here. Let Cjr(t) be the tons of carbon emitted per unit of a com-modity j in region r at time t, and yjr(t) be the total volume of commodityj produced by the industry in region r at time t. Then, the total carboncontent Tjr is:

Tjr = Cjr(t)yjr(t) =∑

ir∈inputsCir(t)x

jrir

(t) (15)

where ir is the set of commodities used in the production of good jr, xjrir

(t) isthe amount of commodity i used in the production of commodity j in region rat time t. Because we will use the same carbon accounting for our simulations,we include time dependence explicitly in all expressions. Our data, takenfrom GTAP, is broken down by industry rather than specific products, so theTjrshould be interpreted as emissions for an industry. Tir(t) = Cir(t)x

jrir

(t) isthe total carbon content of a particular input into the production of goodsin the industry j.GTAP data requires us to use expenditures rather than volumes, so we

have to restate (15) in terms of expenditures. Letting xjrirand yjr be the base-year volumes from the dataset and xjrjr(t) and yjr(t) be the time-dependentchanges in inputs and outputs respectively, we can write:

Tjr = Cjr(t)yjryjr(t) =∑

ir∈inputsTir(t)

xjrirxjrjr

(t)

yjryjr(t)(16)

We typically do not know volumes xjrir or yjr but we do know base yearexpenditure and revenue data for each industry, ejrir and Rir. To use thisdata, note that:

xjriryjr

=pirx

jrir

piryjr=ejrirRir

= Φjrjr

(17)

Therefore, we can write:

Tjr(t) =∑

ir∈inputsTir(t)Φ

jrjr

xjrir (t)

yjr(t). (18)

We can interpret (18) as saying that the total emissions in an industry isthe total emissions for all input industries multiplied by the demand sharefor that input in the base year, adjusted for percent changes since the base

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year. We could solve this system of equations for given Φ, x, and y. Thissystem has more variables than equations due to the land, labor, and capitalfactors. To solve the system, we would ignore the contribution of these factorsby fixing their amounts to zero, leaving us with a square system of equationshave zero as a solution. To simplify the problem, we approximate a solutionby constructing a hierarchy of carbon contributions:

• primary direct carbon is emitted from consumption of crude energycommodities (coal, oil, and gas);

• secondary direct carbon from the consumption of processed crude pe-troleum products such as gasoline and petroleum coke;

• primary indirect carbon from consumption of electricity;

• secondary indirect carbon from consumption of energy-intensive ma-terials such as steel, chemicals, cement, and nonferrous metals. Wealso include other secondary indirect carbon contributions from lessenergy-intensive industries.

We ignore tertiary contributions from the use of factors such as capitaland labor.

3.1 Primary direct emissions

Accounting for primary direct emissions is relatively straightforward, sincethe carbon content of these fuels is constant, and we have data on the volumeof fuel that is consumed by each industry in the base year. For our purposesthe emissions factors for coal, oil, and gas are well approximated by

Ccol = 25kgC/GJ Coil = 21kgC/GJ Cgas = 15kgC/GJ

From these emissions factors and the 2004 GTAP fossil volumes database,a collection of sector- and region-specific energy volume flow data, we obtainthe total carbon budgets for these sectors,

T(t)colr

= 25ycolry(t)colr

T(t)oilr

= 21yoilry(t)oilr

T(t)gasr = 15ygasry

(t)gasr

where the ycr are obtained from the fossil volumes database. These areadjusted for imports and exports of fossil fuels for each industry.

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3.2 Secondary direct emissions and indirect emissions

Once we know direct carbon for each nonfossil good, such as steel, chemicals,cement, manufacturing, etc., we can estimate secondary direct and indirectcarbon by partitioning the direct carbon embedded in each domestic non-crude commodity (and imports) based on demand shares. That is the totalindirect carbon in an output good is the sum of the direct carbon for eachinput industry multiplied by the demand share of that input used by theoutput. Specifically

T indjr (t) =∑

i∈inputsT dirir (t)φjrir

xjrir (t)

yir(t)(19)

Equation (19) in our actual calculations includes an adjustment for importedindirect emissions, which we omit here to simplify the presentation. We theniterate this procedure using the direct plus indirect embedded carbon foreach good:

Tjr(t) = T dirjr (t) +∑

i∈inputs

(T dirir (t) + T indir (t)

)φjrjrxjrir (t)

yir(t)(20)

3.3 Estimates

Table 1 (calculated from GTAP data for the 2004 base year) presents theresults, showing where carbon emissions are produced, how they are traded,and where they are consumed, measured in million metric tons (mmt) ofcarbon.3 We have collapsed the regional detail from 16 to 8 for ease of use;“JAZ”includes Japan, Australia and New Zealand, “CHK”includes Chinaand South Korea, “LAM” is all of Latin America including Mexico, theCaribbean, and South and Central America, and “ROW”includes all othernon-Annex B regions: Africa, the Middle East, and South and SoutheastAsia. The other labels denote USA, the European Union, Russia, and Canadarespectively.Note that these tables do not include direct imports or exports of fossil

fuels because the tax in CIM-EARTH is imposed midstream: for petroleum,the tax is imposed at the refinery; for coal, the tax is imposed when burnedin electricity generation or industrial use; and for natural gas, the tax is on

3To convert these numbers to carbon dioxide emissions, multiply by 44/12.

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distribution or industrial use. Therefore, no border taxes are needed for theimport or export of fossil fuels and they are not included in our calculations.The rightmost column in the table gives the total carbon emitted in a

region from domestic production, which is the standard measure of emis-sions. Each off-diagonal element in the row gives the amount of virtualcarbon exported in the given bilateral flow. Elements on the diagonal arethus “domestic carbon”consumption, that is, the amount of carbon that isboth produced and consumed in the local market. The last row is the sumof domestic carbon consumption and imported virtual carbon consumptionfrom each bilateral trade flow and, therefore, is equal to domestic consump-tion of carbon. The lower right corner gives the total emissions entering theatmosphere.The biggest consumer of carbon in 2004 is the U.S., followed closely by

China and the EU. China is the biggest producer in 2004, followed closelyby the U.S. Note that the United States gets just over 20% of its consumedcarbon from imports, and exports only about 13.5% of the carbon it emits inproduction, which is substantially lower than other developed regions (onlythe EU, with 25% of carbon imported and 13.5% exported, comes in muchbelow 30% in either category), probably because of the high carbon contentof U.S. electricity and the lack of trade in that sector.

Table 1: 2004 Carbon Accounting, in mmt of carbon2004 Annex B Non-Annex B

USA EU RUS JAZ CAN CHK LAM ROW Prod.USA 4618 209 5 70 119 77 161 80 5340EU 223 4053 33 448 19 57 44 205 4683RUS 57 261 1401 15 2 62 18 75 1891JAZ 47 46 2 1335 4 99 7 60 1600CAN 156 22 1 5 340 8 6 7 545CHK 321 329 19 236 28 4578 65 299 5875LAM 197 84 4 12 11 24 1067 29 1427ROW 192 444 23 209 14 270 42 34768 4663Cons. 5811 5449 1493 1927 537 5175 1410 4222 26024

This data is in terms of gross flows. For example, the U.S. imports 223mmt from the EU and exports 209 mmt to the EU. We can represent thesame flows in terms of net imports or exports, so the U.S. imports a net

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of 14 mmt from the EU. Overall, the U.S. imports a net of 471 mmt. Ifthe U.S. imposed a production tax with border tax adjustments, leavingaside behavioral changes, the net border tax receipts would be the tax ratemultiplied by this amount. Table 2 provides the net amounts.

Table 2: Net carbon flows in 20042004 Annex B Non-Annex B

USA EU RUS JAZ CAN CHK LAM ROWUSA - -14) -52 23 -37 -244 -35 -112EU 14 - -223 -3 -4 -272 -40 -239RUS 52 223 - 14 2 43 14 51JAZ -23 3 -14 - -1 -137 -5 -149CAN 37 4 -2 1 - -20 -5 -7CHK 244 272 -43 137 20 - 41 28LAM 35 40 -14 5 5 -41 - -14ROW 112 239 -52 149 7 -28 14 -Net imports 471 767 -398 327 -7 -700 -17 -441

We can see that largest net loser, in absolute amounts, from adding bordertax adjustments to a production tax is China while the largest net winner isthe EU. All non-Annex B countries would be hurt by border tax adjustments.This data is consistent with the observation in the simple analytic model thata production tax favors countries with large endowments of energy comparedto a consumption tax and the results in Matto, et al. Russia is the only AnnexB nation with substantial net exports of carbon.

4 CIM-EARTH

CIM-EARTH is a newly developed, open-source, CGE model of the worldeconomy. We offer a brief introduction here. Details are available at www.cim-earth.org.

4.1 Basic structure of CGE models

CIM-EARTH includes industries that hire labor, rent capital and buy inputsto produce outputs, choosing from feasible production schedules to maximize

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profit. Consumers maximize utility by choosing what to buy subject to theconstraint that purchases cannot exceed income. Income comes from labor(which is fixed in the current application except for exogenous populationgrowth, productivity increases are exogenous) and from capital (includingproducer profits).Like other CGE models, CIM-EARTH is built from repeated application

of nested constant-elasticity-of-substitution (CES) functions that representproduction relationships, consumer preferences, and import demands:

y =

(∑i

αi (γixi)σ−1σ

) σσ−1

(21)

where y is an output, xi are the input factors ranging from labor and capitalto seeds and fertilizer, γi are effi ciency units that determine how effectivelythese factors are used, αi are share parameters, and σ controls the degreeto which the inputs can be substituted for one another. Key parameters ofthe CGE model used here include the elasticities of supply for fossil fuels,the substitution across fossil fuels used in production of energy-intensivegoods, and the trade elasticities for substitution across different locations ofproduction.As noted in our calculations of embedded carbon, the GTAP base-year

data used in this study only has revenues and expenditures rather than quan-tities. Making a similar change in variables, we formulate the general equi-librium problem using the calibrated form of the CES functions:

y

y=

(∑i

θi

(γixixi

)σ−1σ

) σσ−1

(22)

where yyis the ratio between the output of the industry in question (or of an

intermediate bundle or aggregator function in a nest structure) and the base-year value for this quantity from the calibration data set, xi

xiare the ratios of

the inputs for commodity i (capital, labor, coal, intermediate bundles) withtheir respective base-year values, and θi are the share parameters with θi>0and

∑i θi=1.

The calibrated share form of the CES function is suffi ciently flexible toallow representation of a wide range of relationships among variables throughchanges in σ. At either extreme (σ=0 or σ=∞) we obtain special cases of theproduction function. For σ=0, we obtain the Leontief production function,

17

yy= mini

{xixi

}, implying that the inputs are perfectly complementary such

that an increase in output requires an increase in all inputs. For σ=∞we obtain the linear production function, y

y=∑

i

(θixixi

), implying that an

increase in output minimally requires an increase in only one input. Anotherspecial case of the CES function used extensively in economics is the Cobb-Douglas function (σ=1):

y

y=∏i

(γixixi

)θi. (23)

With this normalization of the production and utility functions, the shareparameters, θi, are fixed and equal to the ratio of the base-year industryexpenditure on input i, ei, with the value of the function output, ry: θi= ei

ry.

The share parameters are used to calibrate the model so that the output isconsistent with data from a base year or base period. The functions incor-porating these share parameters are then nested to form representations ofthe various industries and consumers in the model.

4.2 Simple Example

To illustrate the operation of the model, we provide a simple example of theproduction of a good that uses materials, energy, capital, and labor as inputs.

Figure 1: Sample nest for production

The nested function structure is typically represented by a graph; a basicproduction nest is shown in Figure 1. Each node of the tree is a CES functionwith a unique elasticity parameter that aggregates the inputs coming intoit from below. The highest-level node then aggregates the two intermediatebundles into the total industry output. In the example, materials and energyare aggregated using a unique choice of σ representing the relative ability to

18

substitute between these factors. Capital and labor are similarly aggregated,and the resulting aggregates, materials/energy and capital/labor are thenaggregated to produce the final good. The industry depicted in this simpleexample is solving the following profit maximization problem (ignoring taxesand γ factors for now):

maxy≥0,xi≥0 py − pmxm − pexe − pKxK − pLxLs.t. y ≤

(αKL(xKL)

σ−1σ + αme(xme)

σ−1σ

) σσ−1

xKL ≤(αK(xK)

σ−1σ KL + αL(xL)

σ−1σ KL

) σσ−1KL

xme ≤(αm(xm)

σ−1σ me + αe(xe)

σ−1σ me

) σσ−1me

.

(24)

After a change of variables and simplification, we arrive at the calibratedform of the optimization problem:

maxy≥0,xi≥0 rpy − empmxm − eepexe − eKpKxK − eLpLxLs.t. y ≤

(θKL(xKL)

σ−1σ + θme(xme)

σ−1σ

) σσ−1

xKL ≤(θK(xK)

σ−1σ KL + θL(xL)

σ−1σ KL

) σσ−1KL

xme ≤(θm(xm)

σ−1σ me + θe(xe)

σ−1σ me

) σσ−1me

.

(25)

The exponents, σ, are set to represent the relationships among these vari-ables. As noted, there is suffi cient flexibility to represent a range of relation-ships through σ.

4.3 Specific structure of CIM-EARTH

The nested structure of the production in this study is loosely based on thatused by the EPPA group. For this study, we use a model configuration withmoderate-scale spatial (16 regions) and sectoral (16 production sectors plus16 importers per region) resolutions and a simple recursive-myopic strategyin which most important drivers of economic growth and development (e.g.,labor productivity and supply, energy effi ciency, land endowment and yield,resource availability) are modeled with exogenous time trends similar to thoseused in other dynamic CGE models. We calibrated the share parametersexclusively with the GTAP version 7 database of global expenditure values.Consumer utility is also represented with a CES nest. They demand

consumption goods and government services and supply labor and capital.

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Consumers are myopic; they only look at their current state and do notanticipate the future. Savings are modeled as a contribution to the presentstate consumer utility, with savings amounts calibrated to historical data.Utility is Cobb-Douglas, implying that a fixed share of consumer income ineach year goes to government services, savings, and consumption. Labor inthe current version of the model is fixed (there is no labor-leisure choice),with exogenous productivity and population growth.The current version of the model uses a basic, perfectly fluid model of

capital with a 4% depreciation rate. Factors of production are fully mobileacross sectors. Technology is exogenous.As noted, carbon taxes in CIM-EARTH are imposed midstream. For

petroleum, the tax is at the refiner; for coal, the tax is when burned inelectricity generation or industrial use; and for natural gas, the tax is eitheron the distribution by the local distribution company or on the industrial userwhere they obtain gas directly. This roughly follows the recommendation inMetcalf and Weisbach (2009) for implementing a carbon tax, and coversvirtually all emissions from fossil fuels.

4.4 Representation of Trade

Trade among regions is handled through importers of each commodity ineach region. The importers buy commodities both domestically and inter-nationally, transport these commodities, and sell the imports to producersand consumers. Domestic production and imports are treated as separatecommodities that are traded in different markets, following the Armingtonapproach used by other CGE models. Armington elasticities are taken fromthe GTAP model.

Figure 2: Basic nest for imported goods

Figure 2 shows the basic nested importer function for the importer of com-

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modity “com”in region r, labeled I.comr. This example has two exportingregions, r1 and r2, for the given commodity. Each bilateral trade flow fromregion r1,2 to region r requires a certain amount of trade-transport services inthe form of land transport (trucks and/or pipelines), air transport, and seatransport. Each region has air, land, and sea transport industries that pro-duce these —and other —services, although importers purchase homogenousversions from global air, land, and sea sectors that aggregate services fromthese individual regions. The coeffi cients of these functions are calibrated tobase-year expenditure and trade flow data from 2004.The transport nest is aggregated with the bilateral import commodity in

a Leontief nest (depicted by right-angled branches), thus ensuring that thequantity of transport services per unit good remains fixed in each trade flow.This function includes base-year expenditures on import and export tariffsfor each trade flow, eE/I ; carbon “values” of the trade flow from region reat time t (see Appendix 6 on carbon accounting for details), TIre (t), taxedat local carbon market rate, pr(t)CO2

, and subsidized at export region carbon

market rates pre(t)CO2for BTA scenarios; and transport costs for each of three

types τ ≡ {lnd,air,sea}.The calibrated form of the importer optimization problem for an importer

in region r is then:

maxy≥0,xi≥0

rpy−(

(er1 + eE/Ir1)pr1 + TIr1 (t)

(pr(t)CO2− pr1(t)

CO2

))xr1

−(

(er2 + eE/Ir2)pr2 + TIr2(t)

(pr(t)CO2− pr2(t)

CO2

))xr2

−∑T∈τ

(er1T pTxr1T + er2T pTx

r2T )

s.t. y ≤(θ1(x1)

σ−1σ + θ2(x2)

σ−1σ

) σσ−1

x1 min(xc1 ,xT1)x2 min(xc2 ,xT2)

xT1 ≤(θland(xland)

σ−1σT1 + θair(xair)

σ−1σT1 + θsea(xsea)

σ−1σT1

) σσ−1T1

xT2 ≤(θland(xland)

σ−1σT2 + θair(xair)

σ−1σT2 + θsea(xsea)

σ−1σT2

) σσ−1T2

.

4.5 Business as Usual Scenario

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Our business as usual scenario has medium population growth, high economicgrowth, abundant fossil fuels availability and use, slow technological change,and slow clean energy adoption. This implies an approximate doubling ofemissions by 2020, as illustrated in Figure 3. Projections from the EnergyInformation Agency are illustrated by black dots and all 40 IPCC projections(from the Special Report on Emissions Scenarios) by gray lines. Our businessas usual scenarios is on the high end of other scenarios but not outside theexisting range.

Figure 3: BAU Emissions; black line is CIM-EARTH, gray lines SRES scenarios,black dots are EIA estimates

While CIM-EARTH is dynamic, here we focus on its predictions at asingle date, the year 2020. Because it has fluid capital and labor across sec-tors but exogenous technological change which does not respond to long-runpressures, we interpret it as a model of the medium-run (5-10 year) response.Table 3 provides a carbon accounting matrix for 2020 based on these es-timates. It also includes estimates of the changes in production and con-sumption over the 2004 baseline. In our business as usual scenario, emissionsincreases are substantially higher in developing countries than in developedcountries. Trade relationships remain roughly the same —most countries

22

increase production and consumption at similar rates.

Table 3: 2020 Business as Usual Scenario and change from 2004 estimates2020 Annex B Non-Annex B ChgeBAU USA EU RUS JAZ CAN CHK LAM ROW Prod. (%)USA 6673 288 11 97 178 171 252 1331 7802 46EU 328 5544 77 62 30 125 74 377 3317 41RUS 121 515 3161 29 5 204 44 191 4270 126JAZ 63 62 3 1821 6 208 12 102 2278 42CAN 257 36 1 8 509 20 11 13 855 57

CHK 752 784 65 486 75 12591 166 761 15680 167LAM 305 137 10 20 19 63 1936 58 2549 79ROW 319 697 52 292 25 667 74 7670 9796 110

Cons. 8818 8063 3379 2815 847 14051 2568 9306 49848 92Chge 52 48 126 46 58 172 82 120 92

The Obama administration set as a goal cutting emissions by 17 percentbelow the 2005 levels by 2020, measured on a production basis. With ourprojected increases in emissions, this means cutting 2020 business as usualemissions by 43 percent. Merely holding 2004 U.S. emissions constant re-quires cutting business as usual emissions by 32 percent. Reducing emissionsglobally requires even more extensive cuts from the business as usual projec-tions because of the substantial increase in emissions in developing countries.We emphasize that there is considerable uncertainty surrounding this

scenario. We present it primarily to give an understanding of the baseline.All of our estimates of the effects of a carbon tax are relative to this scenario—to the extent that this scenario is higher or lower than it should be maymatter little to the relative comparisons we use below.

5 Tax Scenarios

We consider four scenarios, each with tax rates ranging from $4 to $48 perton CO2 ($15 to $175 per ton C): (i) a carbon tax applied uniformly acrossthe globe; (ii) a carbon tax applied to production in Annex B countries only;(iii) a carbon tax applied to production in Annex B countries, with completeborder tax adjustments; and (iv) a carbon tax on production in Annex B

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countries with a border tax on imports but no rebate on export (partialborder taxes).We begin with a comparison of the simple analytic model to CIM-EARTH,

showing the uniform tax on carbon necessary to produce a given reduction inworldwide emissions, shown in Figure 4. We calibrate the simple model forthe price of the energy-intensive good per ton of embodied carbon as $230,about three times what it would be if the energy-intensive good were coal.Setting α = 0.05, and β = 0.8 allows us to compute the necessary tax ratesfor the simple model. The highest tax rate we consider, just under $50/tonyields a 38% reduction in emissions, which is not suffi cient to keep globalemissions constant at 2004 levels. Note the pronounced nonlinearity in thisrelationship as additional cuts require ever greater increases in the tax rate.The simple model has less curvature because CIM-EARTH has many marginson which carbon can be reduced, with the least costly margins respondingfirst as tax rates rise. A critical margin turns out to be the reduction in theuse of coal, which accounts for 80 percent of the decline in global emissionsat low tax rates, falling to 60 percent at the highest tax rates we consider.

Figure 4: Emissions reductions from a global CO2 tax, CIM-EARTH and SimpleModel

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Figure 5 shows projected reductions in global emissions under differenttax scenarios. The lower line marked “UN” is the same line as the CIM-EARTH line in Figure 4. The upper line, marked “AB,” is the response ofglobal emissions to an Annex B production tax. A tax imposed only in AnnexB countries generates a little more than one-third the emissions reductionsachieved with a global tax, largely reflecting the importance of non-Annex Bcountries in world production of CO2 emissions by 2020 (as shown in Table5).

Figure 5: Annex B and global emissions redutions under various tax rates

The line marked “ABAB”indicates the contribution of Annex B countriesto the reduction in global emissions, the reduction in emissions from AnnexB without offsetting the increases in emissions elsewhere. This contributionexceeds the overall reduction because non-Annex B countries increase CO2

emissions under the Annex B production tax. The increase in emissions bynon-Annex B countries relative to the reduction by Annex B countries, thestandard measure of carbon leakage, ranges from roughly 15 percent at lowtax rates to over 25 percent for the highest tax rate.

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The line marked "ABBTA" shows the effects of border tax adjustments.The source of leakage changes from shifts in production from taxing regions tonon-taxing regions to increases in consumption in non-taxing regions. Leak-age is half as large with border taxes than without; as the simple modeldemonstrates, border taxes cannot eliminate all of the carbon leakage be-cause under a consumption tax, there will be increases in consumption innon-Annex B countries.Figure 6 shows emissions reductions in the United States. An Annex

B production tax of about $50 per ton CO2 leads to a nearly 39 percentreduction in emissions from BAU in 2020. This is suffi cient only to reduceemissions marginally from 2004 levels. In contrast, a uniform tax appliedglobally at that same tax rate produces a 33 percent reduction from 2020BAU. The Annex B production tax produces larger emissions reductionswithin Annex B because it is aided by production shifts associated withcarbon leakage. Adding a border tax shifts the U.S. to a consumption tax.The resulting emissions are slightly higher than the emissions from the U.S.under a global tax, as seen in the line labeled ABBTA. This is because globalconsumption will be higher under an Annex B-only tax than with a globaltax, and U.S. production is correspondingly also higher.The full carbon accounting matrices provide additional detail. Table 4

compares an Annex B production tax of just under $30 ton of carbon dioxide($105 per ton of carbon) to our business as usual estimates. The simplestway to read this chart is to consider the four main blocks. The upper-left block of the matrix shows the effects internally to Annex B. It showsa decrease in domestic carbon consumption (the diagonal elements) as wellas a decrease in trade among the Annex B nations. The lower-right blockshows the effects internally to the non-taxing regions and shows an increase indomestic carbon consumption as well as an increase in trade. The lower-leftblock shows the increase in exports from the nontaxing regions into the taxingregions and the upper-right block shows a decrease in exports in the otherdirection. Overall, carbon consumption in the taxing regions falls more slowlythan carbon production due to carbon leakage; production increases in thenon-taxing regions. As predicted by the basic analytic model, consumptiondeclines everywhere, with the exception of a very small increase in ROW (ananomaly with respect to the simple model).We can compare these results to a global production tax, as shown in Ta-

ble 5. The global tax leads to a substantial reduction in emissions comparedto the Annex B only tax (depicted as a positive number here because the

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Table 4: Annex B production tax at $29/ton CO2 v. business as usual.Percent chanages are in brackets.AB-29 Annex B Non Annex Bvs. BAU USA EU RUS JAZ CAN CHK LAM ROW Prod.

USA-1937 -66 -3 -29 -45 -53 -86 -45 -2264(-29) (-23) (-26) (-30) (-25) (-31) (-34) (-34) (-29)

EU-83 -1232 -17 -13 -6 -34 -20 -127 -1531(-25) (-22) (-22) (-21) (-19) (-27) (-27) (-34) (-23)

RUS-46 -179 -930 -10 -2 -97 -22 -80 -1367(-38) (-35) (-29) (-36) (-35) (-47) (-51) (-42) (-32)

JAZ-11 -11 -1 -535 -2 -63 -3 -32 -658(-18) (-17) (-21) (-29) (-24) (-30) (-26) (-32) (-29)

CAN-61 -7 0 -2 -118 -5 -2 -3 -199(-24) (-20) (-19) (-21) (-23) (-23) (-24) (-24) (-23)

CHK42 50 6 37 5 30 12 28 211(6) (6) (8) (8) (7) (0) (8) (4) (1)

LAM131 27 4 1 7 3 102 4 280(43) (20) (37) (7) (35) (5) (5) (8) (11)

ROW62 161 9 72 4 42 11 292 653(19) (23) (17) (25) (15) (6) (15) (4) (7)

Cons.-1902 -1256 -933 -479 -156 -177 -8 36 -4876(-22) (-16) (-28) (-17) (-18) (-1) (0) (0) (-10)

27

Figure 6: US Emissions from production under various scenarios

table compares the Annex B tax to the global tax). Most of the change isdue to domestic carbon in CHK and ROW, which goes down dramatically.Exports from non-Annex B regions to Annex B regions go down by a largeamount as well. Overall CHK production of carbon goes down by 72% rel-ative to the case with only an Annex B tax. Annex B production is higherwith a global tax than a pure Annex B tax, reflecting a reduction in leakage.Annex B consumption is lower by an amount that is more than the increasesin production (in all cases except Russia).Table 6 examines the consequences of introducing a full border tax ad-

justment to the Annex B production tax (turning the production tax intoa consumption tax), comparing it to an Annex B production tax at thesame rate. Production rises in Annex B regions, for both domestic car-bon (upper-lefthand block) and exported carbon (upper righthand block),and falls elsewhere as the BTA halts production-side leakage. Furthermore,while consumption declines in Annex B, it rises (modestly) elsewhere. Fullexport and import BTA’s in coalition countries leads to dramatic changes

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Table 5: Annex B production tax at $29/ton CO2 v. global production tax.AB-29 Annex B Non Annex B

vs. UN-29 USA EU RUS JAZ CAN CHK LAM ROW Prod.

USA-204 -4 0 -11 -3 -16 -38 -17 -293(-4) (-2) (0) (-14) (-2) (-12) (-19) (-16) (-5)

EU-37 -206 0 -2 -1 -11 -7 -61 -326(-13) (-5) (1) (-4) (-4) (-11) (-12) (-20) (-6)

RUS-14 -35 -37 -5 0 -43 -8 -32 -175(-16) (-9) (-2) (-20) (-8) (-29) (-27) (-22) (-6)

JAZ3 4 0 -118 0 -16 0 -3 -130(6) (10) (8) (-8) (7) (-10) (-4) (-5) (-7)

CAN-15 0 0 0 -11 -1 0 -1 -28(-7) (1) (1) (-2) (-3) (-6) (-3) (-6) (-4)

CHK346 373 34 224 37 5239 82 338 6672(77) (81) (92) (75) (86) (71) (85) (75) (72)

LAM180 52 5 5 10 15 500 14 780(70) (46) (54) (30) (63) (29) (33) (28) (38)

ROW142 327 21 122 11 193 31 2628 3476(60) (62) (54) (51) (58) (38) (57) (49) (50)

Cons.401 510 23 215 43 5361 558 2866 9977(6) (8) (1) (10) (7) (63) (28) (44) (29)

29

Table 6: Full border taxes v. no border taxes for Annex B production taxat $29/ton CO2.Full BTA-29 Annex B Non Annex Bvs. AB-29 USA EU RUS JAZ CAN CHK LAM ROW Prod.

USA228 12 1 22 10 8 33 8 321(5) (5) (11) (33) (7) (7) (20) (9) (6)

EU73 251 9 6 2 1 3 31 376(30) (6) (14) (12) (9) (1) (6) (12) (7)

RUS16 8 -15 4 0 178 23 123 338(21) (2) (-1) (23) (-2) (166) (106) (112) (12)

JAZ2 -1 0 129 0 2 0 -2 131(4) (-3) (11) (10) (2) (1) (2) (-2) (8)

CAN41 1 0 0 16 1 1 1 61(21) (3) (13) (7) (4) (5) (11) (10) (9)

CHK-208 -248 -31 -167 -29 67 17 54 -545(-26) (-30) (-44) (-32) (-36) (1) (9) (7) (-3)

LAM-248 -49 -7 -3 -11 -7 -37 -5 -367(-57) (-30) (-51) (-13) (-44) (-11) (-2) (-8) (-13)

ROW-113 -274 -19 -125 -8 -55 -2 -163 -758(-30) (-32) (-31) (-34) (-26) (-8) (-2) (-2) (-7)

Cons.-210 -300 -62 -133 -20 195 37 48 -444(-3) (-4) (-3) (-6) (-3) (1) (1) (1) (-1)

in bilateral carbon flows, with Annex B countries cutting CO2 imports fromnon-Annex B countries substantially; for example, the U.S. cuts carbon emis-sions from China by 26% and from Latin America by 57%. Global emissionsstay roughly the same as we saw in Figure (5).Table 7 presents the results from our final scenario, partial BTA’s (a tax

on imports but no rebate on exports). Once again, we compare the results tothe production tax in Annex B countries at the same rate. Domestic carbonproduction for Annex B countries is somewhat lower than when there arefull BTA’s. Similarly, Annex B carbon imports from non-Annex B countries(lower lefthand block) also fall, compared to full BTA’s. Annex B exportsto non-Annex B countries, however, changes. These go down relative to theproduction tax even though their tax treatment has not changed (in bothcases, there is a tax when carbon is emitted in domestic production but not

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Table 7: Partial border taxes (tax on imports, no rebate on exports) v.Annex B production taxPartial BTA-29 Annex B Non Annex Bvs. AB-29 USA EU RUS JAZ CAN CHK LAM ROW Prod.

USA233 12 1 22 10 -21 -14 -12 229(5) (5) (7) (33) (7) (-18) (-9) (-14) (4)

EU76 273 4 7 2 -18 -7 -36 302(31) (6) (7) (14) (10) (-20) (-13) (-14) (6)

RUS25 44 42 7 0 -17 -2 -11 90(33) (13) (2) (40) (12) (-15) (-9) (-10) (3)

JAZ2 -1 0 134 0 -33 -1 -12 90(5) (-2) (4) (10) (3) (-22) (-14) (-17) (6)

CAN39 1 0 0 17 -3 -1 -1 53(20) (2) (7) (7) (4) (-20) (-12) (-15) (8)

CHK-224 -265 -34 -176 -30 181 27 89 -432(-28) (-32) (-48) (-34) (-38) (1) (15) (11) (-3)

LAM-253 -52 -7 -3 -12 -2 22 1 -306(-58) (-32) (-54) (-15) (-46) (-2) (1) (1) (-11)

ROW-119 -289 -21 -130 -8 5 7 34 -521(-31) (-34) (-35) (-36) (-28) (1) (8) (0) (-5)

Cons.-221 -276 -15 -138 -20 93 30 52 -495(-3) (-4) (-1) (-6) (-3) (1) (1) (1) (-1)

rebate at the border). The reason is likely that the partial border tax pushesdown the price of energy-intensive goods in the foreign market, making itmore diffi cult for Annex B producers to compete in this market (since theydo not get a border tax rebate). With this exception, the overall patternsare similar to the case with full BTA’s: Annex B carbon consumption goesdown and production goes up, relative to a production tax, and the patternis reversed for non-Annex B regions. Global emissions are about the sameas with full BTA’s. Note the substantial trade-chilling effect of the partialborder taxes: both Annex B exports and Annex B imports are lower thanwith full border taxes.

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6 Conclusion and Research Agenda

Using a simple CGE model, we have obtained preliminary results that, forthe most part, confirm our intuitions concerning the impact of carbon leakageon production and consumption in different regions. To obtain more crediblequantitative projections of the impact of carbon policies, we need a bettermodel. The CGE model used here shares many of the shortcomings of othermodels that have been used to study climate change policy.Given the importance of the questions being asked of these models, we

lay out a research agenda for continuing improvements in four critical dimen-sions: parameter estimation, static structure, dynamics, and policy alterna-tives.

• Parameter estimation. Parameters in our model are taken from theGTAP database and from the EPPA model. An important researchquestion is the sensitivity of our results to these parameters. As apreliminary matter, we intend to conduct sensitivity analyses, suchas using higher Armington elasticities that would make trade moresensitive to relative prices. In addition, we intend to use the GTAPdata reflecting price differentials across countries, combined with tar-iffs and freight rates, for empirical estimation of the relevant elastic-ities. We are also interested in the robustness of our results to in-put data and parameter uncertainty. The GTAP data from whichwe compute our share parameters, and also other parameters used inour model (e.g., CES elasticities), are all somewhat uncertain. Weplan to study how robust are our results to this uncertainty. In otherwork we have used large-scale parameter sweeps for this purpose. Seehttp://cimearth.org/files/sensitivity-draft.pdf.

• Static structure. The current model has an essentially static structurethat is limiting in a number of ways. It does not deal well with theextensive margin where a nation begins to import from a region forwhich its trade share is currently zero. Also, because of the staticstructure of the model, we have interpreted our results as representingthe possible effects of carbon taxes in the medium term. A dynamicmodel will allow us to compare short- and long-term responses. Morefundamentally, agents are not forward-looking, so they do not antici-pate future climate policies, such as changes in tax rates or the possible

32

future imposition of border taxes. A dynamic model will allow agentsto anticipate future policies, possibly giving a better understanding ofhow leakage and border taxes affect incentives to join a climate treaty.

• Dynamics. Our model does not fully account for the impact of techno-logical change on carbon emissions. Di Maria and van der Werf suggestthat induced technological change following imposition of a carbon taxcan reduce carbon leakage (by decreasing the carbon content and hencethe price of goods produced in a country subject to taxation), and even(if induced technological change is suffi ciently large) reduce emissionsin countries that are not subject to taxation. We are actively pursuingthese important research directions.

• Policy alternatives. The current model is limited in its ability to repre-sent likely border tax regimes. We estimated a system in which bordertaxes were imposed based on the importing country’s emissions, butthis estimate was based on the emissions per unit of value in the im-porting country, not per unit of volume, as would likely be the casein actual implementation. Using volumes, however, requires specifyingvarieties of goods; and getting consistent definitions across countriescan be problematic. Nevertheless, modeling more realistic border taxesshould be feasible.

In the longer run, it would be desirable to have a better representationof trade than the Armington model. It is not clear that this will be possiblein the current CGE structure, in large part because of data limitations. Forexample, different trade representations might need firm-level data, whichmay not be available at a suffi ciently broad level to use in a global CGEmodel.

References

[1] Joseph Aldy and William A. Pizer, The Competitiveness Impacts ofClimate Change Mitigation Policies, The Pew Center on Global ClimateChange (2009).

[2] Mustafa H. M. Babiker, Climate Change Policy, Market Structure, andCarbon Leakage, Journal of International Economics 65 (2005), no. 2,421—445.

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[3] Mustafa H. M. Babiker and T.F. Rutherford, The Economic Effects ofBorder Measures in Subglobal Climate Agreements, The Energy Journal26 (2005), no. 4, 99—126.

[4] Paul Demaret and Raoul Stewardson, Border tax adjustments underGATT and EC law and general implications for environmental taxes,Journal of World Trade 28 (1994), no. 4, 5—66.

[5] Robert C. Feenstra, Advanced International Trade: Theory and Evi-dence, Princeton University Press, 2004.

[6] Gavin Goh, The World Trade Organization, Kyoto and energy tax ad-justments at the border, Journal of World Trade 38 (2004), no. 3, 395—424.

[7] Roland Ismer and Karsten Neuhoff, Border tax adjustment: a feasibleway to support stringent emission trading, European Journal of Law andEconomics 24 (2007), no. 2, 137—164.

[8] Ton Manders and Paul Veenendaal, Border tax adjustments and the EU-ETS, a Quantitative Assessment, CPB Documents 171 (2008).

[9] Aaditya Mattoo, Arvind Subramanian, Dominique van der Mensbrug-ghe, and Jianwu He, Can Global De-Carbonization Inhibit Developing-Country Industrialization?, SSRN eLibrary (2009).

[10] Gilbert E. Metcalf and David Weisbach, The Design of a Carbon Tax,Harvard Environmental Law Review 33 (2009), no. 2, 499—556.

[11] Offi cial Journal of the European Union, Directive 2009/29/ec of the eu-ropean parliament and of the council of 23 april 2009 amending directive2003/87/ec so as to improve and extend the greenhouse gas emission al-lowance trading scheme of the community, OJ L 140 (2009).

[12] Joost Pauwelyn, US Federal Climate Policy and Competitiveness Con-cerns: The Limits and Options of International Trade Law, NicholasInstitute for Environmental Policy Solutions Working Paper 702 (2007).

[13] F. Sindico, The EU And Carbon Leakage: How To Reconcile BorderAdjustments With The WTO?, European Environmental Law Review17 (2008), no. 6.

34

Appendix A

We present here a more complex explanation of the calculation of the car-bon matrices. We want to determine the amount of carbon “embedded”inbilateral trade flows from region r to ri of each commodity jr (commodity jproduced in region r):

Cjr(t)xrijr

(t) (26)

where C is carbon content in tons/unit commodity. To calculate the carboncontent Cjr(t) of the output, we sum the carbon content of the inputs usedin the production processes. Therefore,

Cjr(t)yjr(t) =∑ir

Cir(t)xjrir

(t) (27)

where ir is the set of commodities used in the production of good jr (thisincludes the domestic good and the imported bundle), xjrir (t) is the amountof commodity i used in the production of commodity j in region r at time t,and yjr(t) is the total volume of commodity j produced by the industry inregion r at time t. For clarity, we include all time dependence explicitly inall expressions.This expression is written in terms of quantities, while most of the data

available is in terms of expenditures. With a change of variables, we obtainan equivalent expression for the carbon content,

Cjr(t)yjryjr(t) =∑ir

Cir(t)xjrirxjrir (t) (28)

where xjrir and yjr are the base-year volumes and xjrir

(t) and yjr(t) are thetime-dependent changes in the inputs and output, respectively.Rather than compute the carbon content of the individual products, we

compute the total carbon budget for the industry measured in terms of thebase-year quantities. In particular, we define the total carbon in a sector

Tjr(t) = Cjr(t)yjryjr(t) (29)

and then

Tjr(t) =∑ir

Tir(t)xjrirx

jrir

(t)

yiryir(t)(30)

35

We typically do not know xjrir and yir . In those cases where we do knowthe volume data for the base year, we compute the ratio directly from thevolume data. In all other cases, we can compute the ratio from the availableexpenditure data

xjriryir

=pir x

jrir

pir yir=ejrirRir

≡ Φjrir

(31)

where the expenditure and revenue data for each industry, ejrir and Rir areknown. Note that if the volume and expenditure data are consistent, theratios computed from either will be identical.Therefore, we have

Tjr(t) =∑ir

Tir(t)Φjrir

xjrir (t)

yir(t)(32)

Now we need to estimate the total carbon budget Tjr(t) for each industry j inregion r at time t. We approximate the total carbon budget by constructinga hierarchy of carbon contributions: primary direct carbon is emitted fromconsumption of crude energy commodities (col, oil, and gas) and secondarydirect carbon from the consumption of processed crude petroleum products(ptl) such as gasoline and petroleum coke; primary indirect carbon fromconsumption of electricity (elc); and most secondary indirect carbon fromconsumption of energy-intensive materials such as steel, chemicals, cement,and nonferrous metals (stl, chm, cem, and nfm). We also include othersecondary indirect carbon contributions from less energy-intensive industries.We ignore tertiary contributions from the use of factors such as capital andlabor.Accounting for primary direct emissions is relatively straightforward, since

the carbon content of these fuels is constant, and we have data on the volumeof fuel that is consumed by each industry in the base year. For our purposesthe emissions factors for col, oil, and gas are well approximated by

Ccol = 25kgC/GJ , Coil = 21kgC/GJ , Cgas = 15kgC/GJ . (33)

From these emissions factors and the 2004 GTAP fossil volumes database, acollection of sector- and region-specific energy volume flow data, we obtainthe total carbon budgets for these sectors,

T(t)colrr

= 25 ycolry(t)colr

, T(t)oilr

= 21 yoilry(t)oilr

, T (t)gasr = 15 ygasry

(t)gasr ,(34)

36

where the ycr are obtained from the fossil volumes database.Some portion of these crude fossils are, of course, exported to various

regions where they are demanded and consumed in the model as importedfossil commodities,

TIcr (t) =∑re

T (t)cre

ΦIcrre

xIcrre(t)

y(t)cre

for c ∈ {col, oil, gas, (35)

where re is summed over all exporting regions that trade the good with regionr and Icr labels the importer of good c in region r.The primary direct emissions in each industry j in region r at time t is

then

T dirjr (t) =∑

c∈col,oil,gas

(T (t)cr Φjr

cr

xjrcr(t)

y(t)cr

+ T(t)Icr

ΦjrIcr

xjrIcr (t)

y(t)Icr

), (36)

and the primary direct carbon in the imported version of good i in region r,I ir, is thus

TIir(t) =∑re

T dirire(t)ΦIir

re

xIirre(t)

y(t)ire

, (37)

for each noncrude fossil good, i ∈ ζnf ≡ {stl,chm,cem,nfm,air,sea,. . . }.We then estimate secondary direct carbon and indirect carbon by parti-

tioning the direct carbon embedded in each domestic noncrude fossil com-modity ζnf and in each imported commodity ζ

Inf ≡ {Istl, . . . , Isea, . . . }, based

on the demand shares

T ind1jr (t) =

∑i∈ζnf∪ζInf

T dirir (t)Φjrir

xjrir (t)

y(t)ir

(38)

We then iterate this procedure using the direct plus indirect embedded car-bon for each good:

Tjr(t) = T dirjr (t) +∑

i∈ζnf∪ζInf

(T dirir (t) + T ind1

ir (t))

Φjrir

xjrir (t)

y(t)ir

. (39)

For technical simplicity, in the current study we calculate the time seriesof the fractional supply and demand flow variables (y and the x) in scenarios

37

that lack BTA (but have the same carbon prices and coalitions), apply thetrajectory as an exogenous input to calculate BTA values in the scenarioswith BTAs, and compare with the time series in the BTA scenarios to confirmthat the assumption is consistent. This simple estimate proves suffi cient forour purposes here.With these approximate total carbon budgets for each good in each re-

gion, the imported carbon due to bilateral trade flow of good j from regionre to region r is

TIir(t) = Tire (t)ΦIirre

xIirre(t)

y(t)ire

(40)

38